I believe the driving factor on how engaged employees are to the business is in direct relation to how inspired they are by the leadership of the company. If good leaders are engaged in inspiring the employees in believing in the values of the organisation then employees will naturally feed off the enthusiasm and will also be engaged (despite any short falls that may appear in bureaucracy, process and systems).
I am sure all organisations have some type of bureaucracy that is unpalatable or distracting to the core business, but I don’t think that is all that new (and existing) employees are looking for when they decide on their future in a company.
I am no psychologist but I think Maslow has a point and it cannot be ignored. I believe that most workers fit into the “safety” hierarchy. I also believe only through great leadership will workers be inspired into the “esteem and above” hierarchy that “engaged” employees dwell in.
Good bureaucracy, management and culture follow good leadership. Take good leadership away and you have a rudderless boat no matter how well bureaucracy, management and culture fit in with a workers comfort zone.
I am not sure but I believe you described good leadership in the logical part of your article.